"What are those 'items' which are elluding us when we perceive the rule 30 output?"

"What else is there besides 'repetition' and 'nesting'....?"

It seems as though:

-it didn't take me long to notice the lack of repetition and the lack of nesting in the rule 30.

So. Did I just perceive using some other form of perception which 'recognizes' not "a lack of repetition" or a "lack of nesting" but something else? (without first scanning for repetition and for nesting)?

How do I know if I really perceived the (what we are calling) "randomness" without the need for first ruling out the existence of patterns, repetition, or nesting.

Is there some pure perception process built into the human which can auto recognize the randomness ??

All of chapter 10 of the NKS book is about this question, in one way or another. The most directly relevant section is probably the bit about texture recognition, starting on page 578, up to page 581. That is of course just one example, but it is a clear one, that shows ways in which we can classify and analyse patterns using essentially "built in" filters as feature detectors of various kinds.

What we are rapidly able to reduce in this fashion we readily distinguish and find, if not simple, at least comprehensible. What we cannot readily reduce with our built in detectors appears to us complicated. Sometimes formal modeling extensions like basic statistics or short mathematical formulae can reduce other cases, but not all that often - the built in detector array is reasonably good compared to what those methods readily offer.

That is the moral of chapter 10, basically. Things mostly look complicated to us because they are - where the second means "do not yield readily even to much more sophisticated forms of analysis", and where "yield" means "reduce to a short, readily surveyed description, simpler than the original".